This invention relates to a method and apparatus for adaptive bit resolution. More particularly, this invention relates to a method and apparatus for adaptive bit resolution in a digital receiver and/or a digital transmitter.
Modem communication systems, such as cellular and satellite radio systems, employ various modes of operation (analog, digital, dual mode, etc.), and access techniques such as frequency division multiple access (FDMA), time division multiple access (TDMA), code division multiple access (CDMA), and hybrids of these techniques.
In a FDMA system, each channel is assigned a specific frequency. In a TDMA system, each channel is assigned a specific time slot in a periodic train of time intervals over the same frequency. Each period of time slots is called a frame. In a CDMA system, different users, base stations (BS), and services are separated from each other with unique spreading sequences/codes.
FIG. 1A is a block diagram of an exemplary cellular mobile radiotelephone system, including an exemplary base station 110 and mobile station 120. The base station includes a control and processing unit 130 which is connected to a mobile switching center (MSC) 140 which in turn is connected to the public switched telephone network (PSTN) (not shown). General aspects of such cellular radiotelephone systems are known in the art. The base station 110 handles a plurality of voice channels through a voice channel transceiver 150, which is controlled by the control and processing unit 130. Also, each base station includes a control channel transceiver 160, which may be capable of handling more than one control channel. The control channel transceiver 160 is controlled by the control and processing unit 130. The control channel transceiver 160 broadcasts control information over the control channel of the base station or cell to mobiles locked to that control channel. It will be understood that the transceivers 150 and 160 can be implemented as a single device, like the voice and control transceiver 170, for use with control and traffic channels that share the same radio carrier.
The mobile station 120 receives the information broadcast on a control channel at its voice and control channel transceiver 170. Then, the processing unit 180 evaluates the received control channel information, which includes the characteristics of cells that are candidates for the mobile station to lock on to, and determines on which cell the mobile should lock.
In a typical digital cellular transceiver, e.g., a mobile station, a received analog waveform signal is digitized in an analog to digital converter (ADC), and an analog waveform for transmission is generated from a digital signal using a digital to analog converter (DAC).
FIG. 1B illustrates a conventional receiver which may be included, for example, in the transceiver 170. The receiver depicted in FIG. 1B is shown in a simplified form for ease of understanding. It will be appreciated that a conventional receiver can comprise additional elements which are not shown or described. The receiver shown in FIG. 1B includes a frequency selective filter 172 (representing the total selectivity in the receiver), having a bandwidth B, and an ADC 174. A received signal is filtered through the filter 172 to, among other things, remove interfering signals, resulting in a signal x(t)=s(t)+nin(t), where s(t) represents the wanted input signal, and nin(t) represents noise. The signal x(t) is converted to digital form in the ADC 174 which includes a Sampler 176 and a Quantizer 178. The Sampler 176 converts the time-continuous portion of the signal into a time-discrete form, depending on a sample clock frequency, and the Quantizer 178 converts the amplitude-continuous portion of the signal into an amplitude-discrete signal by quantizing the amplitude domain into a fine number of fixed distinguishable levels, each a distance Q apart. The process of quantizing is irreversible, since, regardless of how small the quantization level Q, an unresolvable uncertainty of xc2x1Q/2 is associated with each quantized amplitude value. Thus, a quantization noise is inevitably associated with all quantized signals.
The receiver ADC bit resolution is determined at least partially by how much deterioration of the input signal is acceptable, e.g., by the signal to noise ratio (SNR) or signal to interference ratio (SIR) in the output signal that results in a certain desired bit error rate (BER). For convenience, the abbreviation SNR is used in the following description to represent either thermal noise or interference noise. Referring to FIG. 1B, the SNR of the filtered input signal x(t) is SNRin, the SNR of the ADC is SNRadc, and the SNR of the resulting digital signal is SNRtotadc.
FIG. 2 illustrates signal and noise levels in the receiver. In FIG. 2, Pnin is the power of the input noise signal nin(t), Ps is the power of the input signal s(t), Dqadc is the the quantization noise power of the ADC, Pntot is the total noise input power, i.e., Pnin+Dqadc, and Px is the power of the filtered signal x(t). Also shown in FIG. 2 are the SNRin, the SNRadc, and the SNRtotadc. From FIG. 2, it can be seen that SNRin is the ratio Ps/Pnin, SNRadc is the ratio Px/Dqadc, and SNRtotadc is the ratio Ps/Pntot. All of these values may be given in decibels (dB).
Note that, in this example, SNRin and SNRtot are negative. In all examples, it is assumed that the minimum SNR to provide an acceptable BER is negative. This is a normal situation in CDMA receivers, in which despreading of the received signal, after the analog-to-digital conversion, increases the SNR by a factor of the processing gain (PG).
The minimum SNR of the signal converted by the ADC (SNRadcmin) which results in a minimum acceptable SNRtotadcmin for a certain performance (BER) can be described by the following equation:                               SNR          adcmin                =                  10          ⁢                      xe2x80x83                    ⁢          log          ⁢                      {                                                            10                                      SNRin                    10                                                  +                1                                                              10                                                            SNRin                      -                      SNRtotadcmin                                        10                                                  -                1                                      }                                              (        1        )            
For a large negative SNRin, i.e., for an input signal that is basically Gaussian noise, Equation 1 can be simplified as follows:                               SNR          adcmin                =                  10          ⁢                      xe2x80x83                    ⁢          log          ⁢                      {                          1                                                10                                      Δ                    10                                                  -                1                                      }                                              (        2        )            
where xcex94 is a degradation of the SNRin, i.e., xcex94=SNRinxe2x88x92SNRtotadcmin.
The SNRadc due to quantization of a discrete signal x(k) can be calculated by the following expression:                     SNRadc        =                              σ            x            2                                Dq            adc                                              (        3        )            
where:                               Dq          adc                =                              ∑                          i              -              1                        M                    ⁢                                    ∫                              x                                  i                  -                  1                                                            x                i                                      ⁢                                                                                (                                          x                      -                                              m                        i                                                              )                                    2                                ·                                  p                  ⁡                                      (                    x                    )                                                              ⁢                              ⅆ                x                                                                        (        4        )            
and where "sgr"x2 is the power of the signal x(t), M is the number of quantization levels in the ADC (M=2r, r=number of bits), mi is the quantized level, xi is the decision level (wherein if xi-1,  less than x(k)  less than xi then x(k) can be approximated with mi), and p(x) is the probability density function for the input signal and can either be approximated by a Gaussian distribution (which is normally the case in a CDMA receiver): X∈ N(0, "sgr"), or the distribution can be continuously estimated.
Table 1 shows exemplary values for SNRadc and corresponding bit resolutions which result in optimum uniform quantization of a Gaussian signal. This is described in by John G. Proakis, Digital Communications, p. 116 (3rd ed. 1995).
For uniform quantization and a xe2x80x9clargexe2x80x9d number of quantization levels, Equation 4 can be approximated as follows:                               Dq          adc                =                              Δ            q            2                    12                                    (        5        )            
where xcex94q is the quantization step size, i.e., xcex94q=xixe2x88x92xi-1.
The required SNRadcmin and the allowed degradation xcex94 of SNRin according to Equation 2 are plotted in FIG. 3. For example, from FIG. 3, it can be seen that a minimum of 16 dB SNRadc is required if 0.1 dB degradation of the SNRin is acceptable. Based on Table 1, this requires a four bit resolution in the quantizer.
The SNRadc and the SNRin which result in a SNRtotadc of xe2x88x926 dB (for a BER of 10xe2x88x923, an Eb/No of xe2x88x923 dB at 1024 ksps, and a bandwidth B of 4.1 MHZ) are plotted in FIG. 4A, according to Equation 1. In FIG. 4A, the SNRadc is plotted for 1 to 6 bit quantization, according to Table 1.
The resolution of an ADC has traditionally been determined by the worst case scenario, i.e., where the power of the wanted input signal s(t) is low, resulting in a low SNRin. The resolution is set so that the quantization noise power Dqadc is much lower than the power of the thermal noise Pn.
For example, assume that SNRin=9 dB is the minimum SNR (SNRmin) which results in a certain BER. Then, to not degrade performance more than 0.1 dB, the SNRadcmin must be 16 dB (from FIG. 3)+9 dB=25 dB. To achieve an SNRadc of 25 dB, then referring to Table 1, the bit resolution of the ADC must be at least 5 bits. This will result in an SNRtotadc of approximately 9 dB. This can be seen with reference to FIG. 4B which shows SNRadc in relation to SNRtotadc.
Now assume that the power of the input signal s(t) is high, resulting in a high SNRin. As shown in FIG. 4C, the SNRtotadc will be much higher than 9 dB, assuming the same bit resolution is used as when s(t) is low. If the resolution is designed for the worst case, then the SNRtotadc will be too good if the SNRin is high. Thus, there is a need to reduce the resolution in order to keep the SNRtotadc constant at a level resulting in an acceptable BER.
In addition, the required resolution for the ADC also depends on various factors other than the SNR, including the input level range, whether or not automatic gain is used in the receiver, the accuracy of the automatic gain (how constant the input level can be kept), the speed of the automatic gain (how well fading is followed), the degree to which the quantization noise deteriorates the total noise factor of the receiver, and the crest factor of the received signal. These factors should also be taken into account.
Similar to the resolution in the ADC, the bit resolution needed for the DAC is determined by various factors, including how much quantization noise can be tolerated, how accurate the modulation has to be (with regard to phase error or error vector magnitude), and the crest factor of the signal to be transmitted.
FIG. 5A illustrates a conventional transmitter which may be included in, for example, a transceiver such as the transceiver 170. The transmitter shown in FIG. 5A includes a Waveform Generator (WFG) 510 and a DAC 520. A digital signal sd(t) having r bits is generated in the WFG 510. This signal is converted into an analog waveform Sc(t) by the DAC 520. The DAC 520 has a signal to noise ratio SNRdac, and the resulting analog signal has a signal to noise ratio SNRtotdac.
The principle for D/A conversion is similar to the principle of A/D conversion. In D/A conversion, a continuous waveform that has an infinite resolution in the amplitude is approximated from a discrete waveform having a finite resolution in the amplitude.
A difference between D/A conversion and A/D conversion is that SNRtotdac only depends on the quantization of the signal. The quantization noise in the transmitter results from quantization in the WFG 510 and the DAC 520. Furthermore, in D/A conversion, the signal to quantize is not approximated as Gaussian. In fact, the amplitude distribution P(x) of the signal to quantize in the DAC are perfectly known by the transmitter.
Equations 3 and 4 are valid for determining the SNRtotdac, substituting SNRtotdac for SNRtotadc and Dqdac for Dqadc. The bit resolution in the DAC 520 does not have to be the same as in the WFG 510.
According to Equations 3 and 4, the quantization noise depends on the statistics of the signal.
A signal with a high crest factor requires a larger number of bits compared to a signal with a low crest factor, assuming the quantization noise is kept constant. To see why this is so, it is helpful to refer to FIGS. 5B and 5C which show signals x1(t) and x2(t), respectively, with different shapes and crest factors having the same power "sgr"x2. For the signal x2(t) that has a large crest factor, the quantization must be such that the signal is not clipped. However, most of the time the signal x2(t) is small. To represent the small part with a given accuracy, a small quantization interval is required. At the same time, the range must be large not to cause clipping. This high range and small quantization interval means that a large bit resolution is required.
The crest factor Fc can be defined as follows:                     Fc        =                              Apeak            Arms                    =                                    max              ⁢                              "LeftBracketingBar"                                  x                  ⁡                                      (                    t                    )                                                  "RightBracketingBar"                                                                                      1                  T                                ·                                                      ∫                    0                    T                                    ⁢                                                                                    x                        2                                            ⁡                                              (                        t                        )                                                              ⁢                                          ⅆ                      t                                                                                                                              (        6        )            
where T is the period of the transmitted signal, Apeak is the peak amplitude of the transmitted signal, and Arms is the effective value of the amplitude.
The crest factor of a transmitted signal depends on the modulation format. A transmitter in a specific system might operate in different modes, where each mode has a different modulation format. Thus, in some of the modes, the crest factor might be very low, enabling use of a low bit resolution, while in other modes the crest factor might be high, requiring a high bit resolution.
Conventionally, the bit resolution and the quantization levels are set to manage the worst case, even if this case corresponds to a mode that is rarely used in practice.
Table 2 shows examples of different traffic cases requiring different bit resolutions in the transmitter.
A high bit resolution consumes current. In order to keep the current consumption as low as possible, it is important to use as low a bit resolution as possible in a transceiver. The current consumption is approximately halved for every bit that the resolution is reduced. In a transceiver where high speed converters are needed, for example a Wideband CDMA (WCDMA) cellular telephone, the converters can be major contributors to the total current consumption. It is therefore important to keep the number of bits used in quantization and in other processing in the transceiver, such as sampling, as low as possible.
It is therefore an object of the present invention to reduce the current consumption in a transceiver. It is yet another object to reduce the bit resolution in a transceiver. These and other objects are met by a method and apparatus for adaptive bit resolution.
According to one aspect of the invention, a received analog signal is converted to digital form. A selector selects the resolution of the analog-to-digital conversion based on a signal quality. The signal quality may be the signal to noise ratio or the signal to interference ratio. The resolution is selected depending on how much better the received signal quality is than what is needed.
According to another aspect of the invention, a digital signal to be transmitted is converted to analog form. The resolution of the digital-to-analog conversion is selected based on a crest factor of the signal to be transmitted. The crest factor may depend on the modulation format of the signal to be transmitted.
The analog-to-digital conversion may be performed in a receiver, and the digital-to-analog conversion may be performed in a transmitter. The transmitter and the receiver may be separate or included in a transceiver with adaptable bit resolution.